1. **State the problem:** We need to find the value of 5 times the sum of 2 and 4 added to 7 times the sum of 3 and 8. 2. **Write the expression:** The problem translates to the expression $$5 \times (2 + 4) + 7 \times (3 + 8)$$. 3. **Calculate the sums inside the parentheses:** $$2 + 4 = 6$$ $$3 + 8 = 11$$ 4. **Substitute these sums back into the expression:** $$5 \times 6 + 7 \times 11$$ 5. **Multiply:** $$5 \times 6 = 30$$ $$7 \times 11 = 77$$ 6. **Add the results:** $$30 + 77 = 107$$ **Final answer:** $$107$$